Question

Uprosc wyrazenie algebraiczne :

a) x(x-5)-(x-y)(x+3y)=

b) -(7a-c)(a+c)-2a(a-c)=

c) -(x-5y)(2x-y)+x(3x-y)=

d) -( (x-y)(x-2y)-5x^2)+2x^2=

e) y(x-5y)-(2x-y)(-x+3y)=

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Answer 1

a)x(x-5)-(x-y)(x+3y)= x^2-5x-(x^2+3xy-xy-3y^2)=x^2-5x-x^2-3xy+xy+3y^2=3y^2-5x-2xy

b) -(7a-c)(a+c)-2a(a-c)=-(7a^2+7ac-ac-c^2)-2a^2+2ac=-7a^2-7ac+ac+c^2-2a^2+2ac=c^2-9a^2-4ac

c) -(x-5y)(2x-y)+x(3x-y)=-(2x^2-xy-10xy+5y^2)+3x^2-xy=-2x^2+xy+10xy-5y^2+3x^2-xy=10xy+x^2-5y^2

d) -( (x-y)(x-2y)-5x^2)+2x^2=-(x^2-2xy-xy+2y^2-5x^2)+2x^2=-x^2+2xy+xy-2y^2+5x^2+2x^2=6x^2+3xy-2y^2

e) y(x-5y)-(2x-y)(-x+3y)=xy-5y^2-(-2x^2+6xy+xy-3y^2)=xy-5y^2+2x^2-6xy-xy+3y^2=2x^2-6xy-2y^2